Passing ship effects – from theory and experiment

OFFSHORE TECHNOLOGY CONFERENCE 6200 North Central Expressway

Dallas, Texas 75206

:THIS PRESENTATION IS SUBJECT TO CORRECTION PAPER

NUMBER

OTC 2368

passing Ship Effects

From Theory and ExperiMent

By

Bruce J. Muga, Duke U, and Steve Fang, Exxon _{Research'and Engineering CO.} @Copyright1975

Offshore Technology Conference on behalf of the American 'Institute of Mining, _{Metallurgical, ad} Petroleum Engineers, Inc. (Society of Mining Engineers, The Metallurgical

Society and Societ) of Petroleum Engineers), American Association of Petroleum Geologists, _{American Institute of} Chemi-cal Engineers, American Society of Civil Engineers, American Society _{of Mechanical Engineers,} Institute of Electrical and

Electronics Engineers, Marine Technology Society, Society of ExpIN ation Geophysicists, and Society _{of Naval Architects ad Marine}

Engineers.

This paper was prepared for presentation at the Seventh Annual Offshore Technology Conference to be held in Houston, _{Tex., May 5-8, 1975.1 Permission to copy is restricted} to an abstract of not more than 300 words. Illustrations ray not be copied, Such use an abstract should contain conspicuous acknowledoment of where and by whom the paper is presented.

ABSTRACT

In the first part of this paper,

two methods are presented for deter=-mination of the flow field induced in the neighborhood of a fixed elliptic cylinder by a movine elliptic cylinder. The first and most rigorous method is an extension of the work by Collatz

(1963) where the cylinders _are

repre-sented by surface source distributions The solution is not limited to identi-cal cylinders as was the case for solution presented by Collatz (1963).,

The method evolves into a numerical procedure which is time consuming and

,:71-1oro rompletc

histories of the loading function are

required.

The second method is less rigorous.

but is inexpensive. _{An analytic rather}

than a numerical procedure is utilized to determine the flow field induced by

the moving cylinder in an otherwise

still liquid. The presence of the

fix-ed cylinder is accountfix-ed for by _a

tan-gentialization procedure. Estimation, of the forces and moments for both

References and illustrations at

_end

of paper

methods is accomplished via application of the eeneralized Bernoulli theorem.

The second part of this paper de-scribes an experimental study carried out at Netherlands Ship iviodel Basin

(7!SHB), the objective of which was the determination of forces induced, by

pass-ing vessels on fully restrained'

(cap-tive) vessels. reduced scale (1:68)

models of supertankers (and/or VLCC's) were utilized for both the captive and passing vessels.

T.nolysi.r., of t!-7,.mosurementc are presented in terms of the dimensionless force ratios, as ordinate and distance along the track of the moving vessel as abscissa. Maximum values of the forces

(and moments) are compared with predic-tions (as obtained from theory) and charts are presented to aid the reader in estimating the effect of underkeel clearances and draft ratios on the

dimensionless force (and moment) ratios.

Wit erlivorsify et Technsl'ogy

Ship HydrathechmiLs Laboratory

Library Mekelweg 2- 2628 CD Delft The Nether an s Phone: 31 15 786373 - Fax 31 15 781836

-INTRODUCTION

Forces induced by ships passing in

close proximity to moored vessels are

of considerable interest to terminal

owners and operators because of the

in-creasing awareness of environmental risks

resulting from mooring system failures

and/or excessive vessel notions.

Inter-action effects of two ships, one passing the other a small distance apart, have

been known on a gross level for many

years. However, it is only

recently

with the appearance of supertankers (and

VLCC's) and the increasing traffic at

certain specialized terminals--that

interest in this problem has been

re-newed.

Traditionally, disturbances resulting

from vessels passing near other moored

vessels have been reduced to an

accept-able level by taking one or more of the following precautions:

Increasing the separation distance

2., Slowing down the offending vessel

Increasing the strength (capacity)

of the mooring system (including

alterations in pretensions, i.e.,

initial state).

The effectiveness of these precautions

was rarely quantified and, until

recent-ly, there was little need to do so.

How-ever, with the development of

specializ-ed facilities for berthing supertankers

often at sensitive locations (harbor

entrances) it became apparent that the

effectiveness of applying these

tradi-tional solutions was unknown in a quanti

tative sense. Thus, the need for a

de-liberate study of passing ship effects

was clearly indicated.

The broad objective

of

the overall

nt-.1d;--is the Hovelnpment

of a sstematic

procedure whereby any specific

ship-mooring system can be evaluated (with

particular reference to individual

moor-ing elements) as the system is exposed 1

to definable passing ship occurrences.

In order to achieve this objective, the

following problem areas (or phases) were

identified,

(a) Prediction of time-varying

forces (and moments) on captive

(fully restrained) vessels due

to passing vessels.

PASSINr4 SH1

(b) Prediction of dynamical behavior

-t./...rr..U.CJ 4668 Ti

(vessel motions and individual line loads) with force (and moment) predictions utilized as external excitations.

(c) Evaluation of loads induced in individual mooring components. The objective of the study reported

on herein is directed toward problem

area (a). In particular, this study

describes the development of a procedure

(based on theory) for predicting force

(and moment) histories induced by yes,

sels passing a captive vessel. The

problem is treated both. theoreticallk

and experimentally.

BACKGROUND AND_LITEaATUUE SURVEY

The problem, as described in

pre-ceding paragraphs, is essentially a,

ship-fluid-ship interaction problem for which little experimental data or

theoretical analyses are available.

Some proprietary reduced-scale model

data and a few qualitative field

ob-servations were available to the authors.

These preliminary data served to

illus-trate the essential three-dimensional nature of the problem and to outline some gross features.

Newton (1960) describe S some mea-surements and qualitative observations pertinent to the present problem,

Collatz (1963) presents a very elegant

two-dimensional (infinite fluid) theory

for the case of a pair of identical elliptical cylinders moving past one

another in an ideal fluid. Recently,

Remery (1974rreports on the analysis

of some model_ test data, and Tuck and

Newman (1974)* present an extended

two-dimensional theory and a development of

the slender body theory for application

to the present problem. In addition

to

the foregoing references which focus I

directly on the problem

of

determining

Llhe muLualli induced fcres aricin? 8

a result of one ship passing another,

there

are

a number of other indirect

references which describe various

anal-yses techniques. Sophisticated

numeri-cal methods--using surface distribution

of sources--constitute the vast majority

of the referred to analysis techniques.

These methods are very expensive to

exploit in terms of computing time;

however, they do have some advantages

as compared with physical model testing.

Unfortunately, these methods do require

details on the hull geometry which might

*Neither reference was available by the

time of completion of the present study.

-0TC 2368

13i1JOE J. 1-;LIGA AND _{STEVE .0-\NG}

not be known, or readily availahle _for

all vessels

of

_interest.

Thus, it seems useful at this state

to articulate the general criteria _for

acceptable solutions and then to develop

the pertinent strategy. The _most

impor-tant criteria which significantly fluenced the direction of the study in-cluded the following:

The procedure _{adopted' should be}

simple and inexpensive _{to apply.}

The procedure should be capable

of being extended to a wide range 1

of problems of _interest.

No premium is to be _{placed on a}

high degree of accuracy. The

de-gree of accuracy required _{is that}

suitable for engineering _purposes.

Therefore, approximate solutions are satisfactory.

The procedure should _{be compatible}

with other existing analytical

studies and consistent _{in terms.}

of the confidence _{that an be}

placed in the results.

With these criteria in mind, it was

clear that neither _{an expensive}

numeri-cal approach _{or ah exhaustive model}

test

program would be acceptable. _{It was}

clear that a simplified _numerical

ap-proch in combination with a limited

num-ber of model _{tests would prove}

most

re-warding and have _{the greatest probability}

of success. _{Thus, attention was}

direct-ed simultaneously _{toward (i)development}

of a simplified

numerical technique

which could' be extended _{to a wide para=}

meter rane, and (ii) conduct of a model test program and analysis of results

obtained therefrom. _{These efforts are}

described in subsequent _{sections of this}

study.

THEORETICAL ANALYSIS As noted in the

previous section, in

order to develop

_{an acceptable}

theoreti-cal procedure, _{some simplifying}

assump-were in order. _{Since the detailed}

hull

geometry would' not be _{known for any}

significant number of _{vessels of interest!,}

the first of _{these assumptions}

involved consideration of a pristatic elliptic cylinder rather than the actual vessel

hull. _{For a tanker hull,}

which

inci-dentially is the _{major vessel hull}

type

of interest, _{this assumption}

_is

a

natu-rally suggestive _{one; the obvious}

simi-larity is quite remarkable. _Moreover.

the ellipse lends _{itself to analytical}

solutions, albeit not _{always in closed}

form. The major disadvantage _{of this}

assumption is that the ellipse _{is symL.}

metric fore and aft whereas the actual hull shape .is non-symmetric.

The second assumption was the

consi-deraticn of infinite fluid _{regions. Thus}

certain boundary influences were not

considered. _{The rigid free surface}

assumption' neglects _{any influence of}

surface wave systems _{as generated by}

the moving; vessel. _{It has been noted}

by a number of _{investigators that if}

the Froude number is _{sufficiently small}

then these free-surface effects can be

safely ignored. _{For this study,}

inter-est centers on very low 7roude number

values. _{Thus, the assumption of the}

rigid free surface is _{quite reasonable..}

The assumption of infinite depth,

how-ever, especially in view of the _finite

vessels' draft, was _{recognized to be of}

limited validity. _{In spite of the}

known (or suspected) _{limitations, it}

was decided to develop the _{theory on}

the basis of zero _{underkeel clearances}

for both vessels and _{to utilize the}

physical model test results _{to correct}

these effects empirically.

The third assumption is _{the ideal}

fluid assumption. _{Thus, potential}

theory--with its extensive development

and broad application--could _be

exploit-ed advantageously for this problem.

Tuck and Newman (1974) _{state that the}

cross-flow separation _{forces-arising}

from viscous effects-ere _{likely to be.}

more important than the free-surface

effects. _{This may be true but since}

the free-surface effects are nil anyway

for our problem, it _{appears that the}

cross-flow separation and forces, are

also nil because of the very low

rela-tive fluid, velocities _{that are mutually}

induced.

To summarize, the focus _{of this}

sec-tion is to briefly outline the

high-lights in the development of a

theore-tical procedure for predicting forces

(and moments) induced _{by prismatic}

elliptic cylinders moving in close

proximity to one another in an infinite ideal fluid.

The procedure to be described in the

following paragraphs _{depends upon two}

different methods for the _{determination}

of the flow field' induced _{in the}

neigh-borhood of a fixed elliptic cylinder

by a moving elliptic _{cylinder. The}

first method is _{an extension of the}

PASSii,G SHIP EFFEUTs

method developed by Collatz (1963) _which

in turn is based on _{an approach}

origi-nally developed by Smith _{and Pierce}

(1958). _{The essential technique is the}

representation of the elliptic cylinders

by surface source distributions. _The

second method is much less rigorous and

accounts for the Presence of the fixed elliptic cylinder by a taneentialization

of the flow field as generated _{by the}

moving elliptic _{cylinderin an}

other-wise unobstructed infinite fluid region.

Once the flow fields have been obtained

by either of the above methods, then _the

time varying forces (and moments) _{can be}

easily obtained from the generalized Bernoulli theorem, or alternatively, from the Lagally theorem.

Analysis via Surface Distribution of

Sources The case of two identical

infinitely long elliptical cylinders

moving one past the other, in an infinite

ideal fluid has been studied in _an

ele-gant manner by Collatz (1963). _This

treatment can be easily extended to a

pair of non-identical cylinders _depicted

in

Figs

1. _{Using notation similar to}

that employed by Colletz, the major

features of this extended treatment _are

highlighted below with reference to

Fig. 1.

The following equation can be derived for a point P located on cylinder A:

alnRBA alni<AA qA 1 1 dS 27

-

ar;

s

A S5 A

=A cos

Bi ₍₁₎

Similarly, another equation _{can be}

de-rived for a point P located on

cylinder 3;

r

-1.

Js

a21-r- -13 27 SA

=3 cos

(2)

where,

dSA and dSg are the surface source

segments having strengths qA and qB,

respectively, on cylinders A and 2, respectively.

RAP., RBB, RBA and RAB are distances

from surface source segments to

points P.

aln11A3

a

_nB

2368.,

n _{are the surface normal}

vectol.,

A' B

on cylinders A and B, respectively. are the angles between the positive x-axis and the normal

surface vector for cylinders _{A and}

B, respectively.

BA, UB are the body velocities in

the positive x-direction of

cylin-der A and 3, respectively.

In the above formulation, subscripts A and B refer to cylinders A and B,

respectively. The first and second

terms account for the contribution _to

-the velocity from -the local source (at

point P) and from the remaining _source

distribution on the body itself,

re-spectively. The third term represents

the contribution to the velocity _{due to}

the presence of the other body. Collatz(1963) assumes that the source distributions on cylinder

sur-faces A and 2 can be described _as

func-tions of the cylinder velocities _BA

and UB in the following form:

gIOPUA

g2*U3

qA49

r". 4"

e( )

q30) =()UA

g4(

))B (4) C

(0)

_{C (0)} where,

C() =

1 + G'( g2( ) 9 cl2 sin29') (3)

Then, Eq. _{1 can be transformed into the}

following

set

of

_equations; 2r

gi*

I (5).

Trr (gi(e)kA, + g2 ( kBA)de= cos 2

0

g30) 2

r ₍₆₎

_f

(83 (e) kAA + g4( 0)1`13A)de= C

2 27

0

and similarly, Eq. (2) can be

trans-formed into the following:

2.7

1

₍₇₎

(g2(e)kBB +g1(e))kAB de= 0

,,

OTC

2r (8) E4Y1+ (4g (0) kBB --' + (0)k,3) de = cos 2 2r

-In Eqs. (5) through (8), the kA.,

A kAB'

kpB,

km

are known functions

or

the geometry of the elliptic

cylin-ders and the source segments and are de-fined as follows; alnF,AA k = b1C1(95) AA _aiy\ kAB = b1C () alnRAB

alnR,

= bC kBB

arip

alnItBA IKEA bC (95) 35A

For our problem, cylinder 13 is

con-sidered to be stationary; thus,

_{UB = 0}

and only Eqs. (5) and (7) need to be

solved. The solution is approached

numerically and facilitated by intro-ducing the following substitution:

.12r

17' g(8)k(9,56)de =

1 E

m

e(e)k(e)

(9) v= 1 0 where 2-1) 9 . m

Then, Eq. 5 becomes

(10)

?1( _mv )1 c/S +e2 )k _(t.)

e=1:1 V

A

V"

- V EA _-cos

To indicate application of Eq. (10) to

discrete nnints on tho _7,1T:fan(' of thn

elliptic cylinder, the subscript k may

be employed and Eq. (10) appears as:

111 vkaAs (0,,

40

2

m1

= cos

(/)

(11)

where 2crk _{k= 1, 2,}

Eq. (7) can be _{similarly written as}

g2(ibk)

cc-g2(eij)k3 (e (/),)+ g1 )1$ (8 96' ) B 11$ . .B V' k 2 _mv=1 0

Eqs. (11) and (12) represent a set of 2m linear equations which can be solved simultaneously using standard library subroutines fror which the functions

glOp)

and g2( ) are obtained. _idith

these functions known, the source distributions on the cylinder surfaces

can be determined with the aid of Eqs. (3) and (4). The remaining task is to evaluate the horizontal fluid particle

velocities u and v. For points on the

surface of cylinder B, the velocities may, in principle, be evaluated from the following relations:

q alriFAB

u =

.1:. +

ljr

2

2,

gA

ax.

d-sA SA B + alnR

273

11

a.

BB dSB - UB B 3 and = 77+

jqA

_ayA3

dSB + 21-T B

_aY

LEda, q.B Dlni A 13 SB

The forces (and moments) induced by

cylinder A as it passes cylinder B can

be obtained directly from the generaliz-ed Bernoulli theorem or alternatively

from the Legally theorem. _{Both lead to}

the same result. From the Bernoulli

theorem

P =

- (vq))2

- P

_dt

(15)

where, pc) is a reference pressure, and

p is the _{local pressure. In Eq. (15)}

the tern (77(T02

_' ;F, the

portion of the induced force and is

ob-tained from instantaneous values u and

v of the hydrodynamic flow field. The

term dtVdt is the 'history" portion of

the induced force (or moment) and is

obtained numerically from successive

evaluations (in time) of the source

distribution functions qB. The forces

and moments are finally _{obtained from}

the definitions

Jr

F= -

p n dS and ₍₁₆₎

s

= -

i

-/-",

p(i-'

_{x -n-') dS} s ,

(17)

OTC 2j68 _{T.NUaA AND STEVE FANC:}

+ g (12) 3

(14)

-"inf:tantancou"

-(13)

Finally, for parametric comparisons, it

has been found useful

_to

_{place the force}

and moment time histories in the following form:

F(t)

eb(UA)2

F (t) M(t)

eb(U102 eb2(UA)2

An example of a result obtained from a computer program based on the fore-going analysis is presented in Fig. 2

in

which

_{the non-dimensional forces}

(and moments) are shown as functions of

time. _{Also shown in Fig. 2, for}

com-parison, are the results obtained from an alternate procedure to be described immediately following.

PASSING SHIP EFFECTS

Analysis via Tangentialization Although the analysis presented in the

foregoing section is very rigorous

mathematically, it is relatively

expen-sive (due to computing time requirements) to utilize for extensive parametric

studies. V:oreover, differences between

real and assumed conditions require that

the computed results be modified in an

appropriate manner prior to practical

application. These modifications

re-flect the need to account for underkeel clearance effects, hull geometry, and, in come cases, the presence of the free surface.

Thus, it appears that the development of another solution method which could be applied with far less expense would

be a worthwhile effort. _{This section is}

concerned with the development of an

alternative method of analysis which

retains most of

the

important features

of the earlier solution method

_but

which

can be carried out at far less expense with perhaps some sacrifice in rigor.

For this purpose, we return to the case of a single elliptical cylinder moving in an infinite irrotational fiuid

which is at rest. _{This situation is a}

classical study for which exact solutions are available, and are exemplified by the pattern of constant potential and streamlines as shown in Fig. 3.

The complex potential of the motion produced by an elliptic cylinder of semi-axes a and b moving with velocity UA in the positive x-direction is given by

1,q = U b

la

b

expEq

A a - b (18)

OTC 2358

where; + j77, and 77 are the ellip,

tical coordinates. The expression _for

the streamlines is given by

iJi

-U b

ja

b expFdsin

A a - b

and that for the velocity potential is

given by

UAb

a +b

a - b ex p{-ticos 77

Suppose now that an object (small relative to the flow field) is placed

in this flow field at point P, some

distance away from the moving elliptic

cylinder. _{We would expect that the flow}

field in the vicinity of the _obstruction

would be modified and that the

obstruc-tion would experience a loading _history

as the cylinder passes by. Whereas

the effect of the moving hydrodynamic

flow field might be very great on the

obstruction, the effect of the

obstruc-tion on the flow field would be very

smell, being virtually nil except in _the

neighborhood of the obstruction. Now, replace thA obstruction by an infinitely long vertical wall parallel

to the motion of the cylinder. The wall

then becomes, in effect, a streamline since no flow takes place normal to it. Alternatively, a similar effect could be achieved by a pair of identical cylinders moving on parallel courses at

constant speeds. The vertical plane

midway between the cylinders is a

streamline corresponding to the vertical

wall. _{The normal velocity is zero and}

the velocity tangential to the wall is

twice that existing when onlyone

cylin-der is moving in an infinite fluid region. The presence of the wall has been to

tangentialize the fluid velocity

com-ponents.

These ideas can be extended (with some modification) to the case when a long slender body is the obstruction. The situation is depicted in Fig. 4

which shows the placement of a fixed

cylinder onto the flow pattern

gener-ated by a moving cylinder in _an

other-wise undisturbed fluid. The interaction

effects are not suggested by Fig. 4 but

they are known qualitativelyas re-ported in the published literature (see

Newton (1960) and Silverstein (1957)). .

The following salient features are noted,

These regions are well illustrated

in

the series of Figs. 5 through 9.

These are rather drastic simplifying assumptions but they may not he too far

in error for the specific problem under consideration--at least for the

para-meter range of interest. Moreover, by

controlling the limits of integration (defining, the regions) in a systematic

As indicated by Fig. 4, there is a pressure field associated with the flow pattern which moves with the cylinder.

The presence of the fixed cylinder causes

an intensification of this pressure

field on the exposed side of the fixed cylinder and an attenuation an the

"leeward" side. Maximum intensification

occurs when the two cylinders are abeam.

Further, three' regions adjacent to the

fixed cylinder can be identified. They

are

The region lying between the cylinders and extending from the forwardmost point on the fixed cylinder to the transverse

center-line of the moving cylinder. This is the region where maximum inten-sification of the pressure field

takes place. As the transverse

centerlines exchange relative positions, then I:egion 1 is

de-fined to lie between the aftermost point on the fixed cylinder up to

the transverse centerline of the moving, cylinder.

Z. The region lying on the leeward side of the fixed cylinder where. maximumattenuation of the pressure

field takes place.

3. The region lying between the cylinders and extending from the transverse centerline of the mov-ing cylinder to the point farthest

,aft on the fixed cylinder. This

region is largely a transition region in which alterations to the pressure field (due to the pre-sence. of the fixed cylinder) vary from the intensification charac-teristic of Ee7,ion 1 to the at-tenuated field of Negion 2. Similar to the situation for

Region 1 as the transverse center-lines exchange relative positions, Region 3 is defined to lie between the transverse centerline of the passing cylinder up to the for-wardmost point of the fixed cylin-der.

BRUCE J. MCA AND STEVE FANG

fashion, any difference between the results predicted by this model and the more rigorous model can be minimized.

Then too, for practical application, any mathematical model however sophisti-cated, is subject to modification to account for differences in the simplify-ing assumptions upon which the model is based and the actual problem of interest. The real value of such models lies not so much in how well the predicted re-sults agree with observed rere-sults but in disclosing the nature of the

govern-ing mechanisms. From this viewpoint,

the simplified model serves a timely and useful purpose.

As noted earlier', the exact theoret-ical solution to the interaction effect between two cylinders passing in close

proximity does not exist. Thus, our

immediate task is to (i) develop ap-proximate expressions for the evalua-tion of the terms necessary to determine the time-varying pressures around the cylinder surfaces, and (ii) develop a compatible computational procedure from which the forces (and moments) can. be computed.

To, accomplish this, ye can examine the expression for pressure as developed from the Bernoulli theorem (Eq. 15). The term (V)2 is the "instantaneous" portion of the induced force (or moment) and is evaluated from a knowledge of the instantaneous values of velocity u and

v of the hydrodynamic flow field. The

velocity distribution on the surface of the fixed cylinder is approximated in the following way:

In 1.egion 1,the fluid particle velocities are taken to be the tangentialized components of the velocities generated by the elliptic cylinder moving in an undisturbed fluid.

In Region 2,the fluid is assumed to be undisturbed; thus, the particle velocities are taken to be zero.

C., In Region 3,the particle velo-cities are assumed to vary from the modifications indicated for Region 1 to those indicated for Region 2.

For the Case of an elliptical cylin-der moving in an infinite undisturbed fluid, the complex velocity is ,given by:

11-= iu - jv (21) and

(22)

The "history" portion of the induced force (or moment) resulting from the

term dT/dt of Eq. (15) may be

approxi-mated from the following derivation. With reference to the fixed system, as shown in Fig. 10, we note that

(1)=ipce-,t). Since d?idt . 0 for fixed

point P, then dVdt

_{wat. To}

evalu-ate the partial time derivative, consi-der a system (x' ,y') moving from an initial position I in the fixed system

,y) and having constant velocity,

Vm = iU + jV. At time t, the position

of the origin of the moving system is

at 0'. For particle P, the position

vector with respect to the moving system

ro' is given in terms of r and t by

..i. S.

= (P,t) = -ro +r ..-(1--i+Vmt)+r (23)

Now, consider (i) to be the potential in

the moving system and therefore it is a

function of r'(x' and y') only. Then,

ait)

at

_at

_at

Since d4D/dr'' is the particle velocity induced by the moving system in an otherwise infinite undisturbed fluid

and

3--,/

at is the velocity of the

moving system, we can write

(24)

acp

= (-q) .

(-In)

= Uu + vv

at

(25)

For our case, U UA and V . 0. Thus,

a_32 Uu ₍₂₆₎

at

The foregoing derivation is based on the assumption that the interaction effects

can be approximated as indicated herein; this is not quite the case when the passing cylinder speeds are high and/or the separation distances are quite small.

With estimates of the pressure p, we are now in a position to determine the time-varying forces and moments from Eqs. (16)and (17), respectively.

rAssiNu snit- r_rrnuis _{O'I'C 23}

For comparison purposes, the _force

and moment time histories can be placed

in non-dimensional form. An example

of the results obtained from _{a computer}

program based on the foregoing analysis is presented in Fig. 2.

EXPERIMENTAL PROCEDURE AND SELEDTED RESULTS

In order to verify and/or determine

the limits of the theoretical _approaches

described in the preceding sections, an

experimental test program was carried out in the shallow water wave tank of

the Netherlands Ship Model Test _Basin,

Wageningen, Netherlands. The model

scale (using tanker hull shapes) was

1:68 and a schematic of the test _{set up}

is as shown in Fig. lie. To make the

results as widely applicable as _possible

the captive model technique was _employed.

For these tests, the stationary or "captive" vessel was restrained in surge, sway and yaw but free to move in heave, roll and pitch.

The moving or "passing" vessel was self-propelled and maintained course via an attached guide frame which rolled

along a track that had been placed on

the floor of the basin. To minimize

any influence of the guide frame, the track was placed on the side of the passing vessel opposite the restrained

vessel.

All

_{of the tests reported on}

herein were conducted at very low

(subcritical) Froude numbers; thus, the Kelvin-type wave pattern was not

ob-served. As the vessel moved past the

stationary vessel, forces in the hori-zontal plane were measured at three locations (two pickups were oriented to sense forces in the lateral direc-tion and one pickup recorded forces in

the longitudinal direction). Water

level variations at six (6) locations

around the vessel

hull

were measured.

(srr F. 11b),

These signals, after suitable fil-tering were resolved into two force

components and one moment. In addition,

distance along the track was monitored at four fixed locations by

photo-electric cells. The analog signals

thus recorded were then digitized and placed on magnetic tape for processing

by computer. _{The quantities given}

herein are generally presented in dimensionless form but the dimensioned quantities can be scaled up to prototype dimensions in accordance with the

Froude model law. _{Thus, the results}

UAb exp

=

(a-b)

c sinh

- [Ab

in

led

he

on,

-ype

oTc L5KUUe. J. MUGA AND STPNE FANG

as presented, are appropriate for

proto-type conditions. Some 47 tests were

conducted to determine the effects of separation distance, absolute velocity, relative velocity (due to the presence

of a current), underkeel clearances (of

both passing and fixed vessels) and different vessel combinations.

These effects are illustrated by comparing the results from a few

select-ed cases. The results are presented in

terms of the time-varying non-dimension-al loading function (as defined in the preceding section) as ordinate with distance along the track as abscissa.

Fig. 12 (Test Nos. 3356 and 3357) demonstrates the validity of utilizing the non-dimensional loading functions as a comparison parameter since the

effect of varying the passing ship speed (in the absence of current) is entirely

accounted for by this parameter. Within

the experimental and data handling error range, the results from the two tests coincide.

Fig. 13 (Test Nos. 3356, 3354 and 3355) shows the effect of separation

distance. In agreement with our

intui-tive notion, the greater the separation distance the smaller the induced forces (and/or moments).

Fig. 14 (Test Nos. 3354, 3348 and 3344) illustrates that increases in the

underkeel clearance (water depth/draft ratios) result in significantly lower induced forces (and moments).

The results from those tests con-ducted in the presence of a current are not so clearly revealing although all of the general trends indicated above

are still present and valid. The reason

for this distinction is as follows: when no current is present, the induced

force is El filnction of the square of the

absolute velocity or the square of the relative velocity since they are the

same. However, when current is present,

the induced forces are a function of a combination of the square of the absolute velocity and the square of the relative

velocity. The specific combination

depends on the relative strengths of the

two force components. The

"instan-taneous" or steady component is a func-tion of the relative velocity whereas the "history" component is a function of

the absolute velocity. Thus, the

non-dimensional loading functions which were Utilized to make parametric comparisons

for Figs. 12 through 15 are not quite appropriate when current is present.

Finally, it is appropriate, at this point, to compare the predictions as obtained from-theory with those measured by experiment for as nearly similar

conditions as possible. Fig. 15

pre-sents the comparison for one case where the following differences between the assumptions (upon which the theory is developed) and the experimental

condi-tions are noted:

Hull geometry (theory assumes elliptic cylinders whereas

experiments were made with model tanker hulls).

Two-dimensional flow for theory versus three-dimensional flow

for experiment. This implies

absence of free surface and infinite draft for theory. Experimental error.

Considering these differences, the agreement indicated by Fig. 15 is

re-markable indeed. Although not shown,

comparisons for other similar cases were made and, in general, agreement between theory and experiment improves with increasing separation distance and with decreasing vessel speeds. ANALYSIS OF TEST RESULTS

Comparisons of many time-histories of loading functions in specific detail

is a laborious and not altogether

re-warding effort. Fortunately, however,

by utilizing certain features of the predicted time-histories as a correlat-ing medium, nearly all of the test

results can be organized into a coherent meaningful pattern.

7irst, not ti,J,t for n11 of the toot

results presented thus far the time pattern (or phase relations) of the occurrence of the peaks and the sequence of the loadings are very similar. This suggests that each loading function can be described by a single value of the ordinate, perhaps the maximum.

Second, the time pattern of the load-ing functions as predicted by theory are all very similar to each other and to their corresponding experimental cases. 1368 zed ter is hes an 4 up -ble >yed.

-nx-tix-

.r.rrLur

Third, the maximum value of the load-ing function as measured can be normal-ized by dividing it by the maximum value of the loading function as obtained from

theory. The latter value is obtained

for the case corresponding to a pair of prismatic elliptic cylinders in an infinite fluid (i.e., infinite draft). The result of this division is termed the dimensionless force (or moment) ratio.

Then, the dimensionless force (or moment) ratio can be plotted as ordinate versus the minimum water depth/draft

(i.e., underkeel clearance) ratio as abscissa. The minimum water depth/draft ratio can be either that for the fixed vessel or the passing vessel and largely

confirms the validity of the

two-dimensional theory. On this basis, the

results of a large number of tests can be presented on a single graph as shown

in Fig. 16, where the effects of separa-tion distance, passing vessel speeds, different vessel combinations, under-keel clearances of either passing or

fixed vessels are all included and taken

into account at once. In Fig. 16,

values of the non-dimensional force (or moment) ratios appear as straight Lines as indicated, on the

semi-loga-rithmic graph. In addition, only those

tests where the current is zero appear in Fig. 16.

A somewhat similar graph (Fig. 17) has been prepared where current was

pre-sent. For all of those cases the

current magnitude was 2 knots. The

major distinction to be noted in com-paring Figs. 16 and 17 is that the

dimensionless force ratio for the lateral force has a different slope dependent

upon whether current is present. This

undoubtedly reflects the fact that the non-dimensional loading function (as defined) is not quite appropriate as a correlating parameter for the reasons cited in the preceding section.

Nevertheless, Figs. 16 and 17 or equivalent representations can be em-ployed to synthesize loading functions for specified passing ship incidents.

From another viewpoint, Figs. 16 and 17 represent corrections (dependent upon the minimum underkeel clearance ratio of either the fixed vessel or passing vessel) that need to be applied to the non-dimensional loading functions as

obtained from theory. It is to be

re-called that the non-dimensional loading functions obtained from theory include the influences of vessel specification,

'OTC 23E8

separation distance, and passing vessel

speed. For engineering purposes, linear

interpolations for conditions lying between those pertaining to Figs. 16 and 17 are appropriate.

FINDINGS

From the results of the study re-ported on herein, it is found that the

forces (and moments) induced by a _vessel

passing a restrained vessel in close proximity depends upon separation dis-tance, absolute and relative velocity, underkeel clearances of either fixed and passing vessels and specific vesel

combinations. The nature of the'de=

-pendency is a very complex one in which all of the variables are interrelated. All other things being equal, the

in-duced forces (and moments) (i) decrease with increasing separation distance,

decrease with decreasing velocities, decrease with increasing underkeel clearances and (iv) increase with in-creasing vessel size.

It was also found that the approxi-mate theory as developed and reported, on herein predicts well the loading functions for the assumed conditions. CONCLUSIONS.

It is concluded that a procedure based in part on theory and on experi-ment can be employed to synthesize load-ing functions appropriate for a vessel passing a restrained vessel, subject to

the following limitations; I

Vessel hulls must be reasonably approximate to elliptic cylinders.

Passing vessel speeds (or alter= natively Froude numbers) must

be sufficiently low to avoid I

development of Kelvin-type waVe

pattern.

Ratio of relative to absolute velocities must lie within the range of ratios reported on

herein.

IOMENCLATURE

8,b major and minor axes of elliptic

cylinder, respectively

b' minor axes of elliptic cylinder

elliptic function ,./a2_b2

8/, g2

surface source distribution functions defined implicitly

83' 84 by Eqs. (3) and (4)

r r. o'

denotes real component of com-plex representation

denotes imaginary component of complex representation

Ic integer index

kAA' kAB functions of geometry of ellip-_{tic cylinders and source}

seg-ments (see Egs. (5-8) and following

rr dummy integer index

n,,n normal surface vector A'

local pressure reference pressure

strength of source segments on cylinders A and B, respectively complex velocity

position vector relative to fixed system

position vector relative to moving system

position vectors relative to fixed and moving systems as defined in Fig. 10

time

horizontal fluid velocity in x-direct ion

horizontal fluid velocity in y-direct ion

complex velocity potential spatial coordinate

spatial coordinate

OKUUt. J. NUGH AND STLVt elm;

A,B subscripts denoting cylinders

A and B, respectively

CO),

functions of geometry of

ellip-CIO)

_{and following}tic cylinders (see Egs. (4) force

F (t), F(t)

M,M(t) moment

point in space

RAA'RBA distance from surface source

R_{AB, BB}R segments to position P (see

Fig.

1

SA' SB surface on cylinder A and B,

respectively

dSA,dSB _{and B, respectively}surface segments on cylinder A

U, BA, cylinder velocities in

x-direction

UB

V cylinder velocities in

y-direction

complex cylinder velocity angle between positive x-axis and normal surface vector for cylinders A and B, respectively

angle defined by Fig. 1

angle defined by Fig. 1

velocity potential function streamline function

mass density integer index

elliptic coordinates

complex elliptic coordinates complex velocity del operator vm

5, 5'

32') (BB'kEA F,Fx(t),

_

-ACKNOWLEDGEMENTS

This study was initially undertaken by the senior

author while he _was

spending a leave of absence (from _Duke

University) with _{the Exxon Research}

and Engineering _Company,

Florham Park,

New Jersey. _{Thus, to Exxon Research}

and Engineering _{Company and in}

parti-cular to the _{Marine Engineering}

Section, Civil and Marine

Engineering Division, Technology Department, must be given acknowledgement for providing

encour-agement and the _{financial support}

to

undertake and complete _{this study.}

The writers also

acknowledge their sincere appreciation to Exxon Research and Engineering

Company for permission

to publish the _{results of this study.}

REFERENCES

1. _{Newton, R.N., (1960),}

'Some Notes

on Interaction Effects _{Between Ships}

Close Aboard in _{Deep Water,"}

Proceedings, First Symposium on

Ship maneuverability, _{DTMB Report.}

1461.

PASSING SHIP EFF1..2TS

2. _{Collatz, C., (1963),}

"Potential

Theoretische Untersuchung _der

Hydrodynamic Schen

Wechselmirhung

Zweier Schittskorper," _Jahrbuch

Schiffsbautechnischen

Gesellschaft, 57, 1963, pp. 281-329

Eemery, C.F.M., (1974), _'Analysis

of Model Tests _{of Passing Ship}

Effects," Proceedings, _Sixth

Off-shore Technology _Conference,

19747,

--Smith, A.M.O., and _{Pierce, I.()}

(1958), "Exact Solution of the

Neuman Problem," _{Douglas Aircraft}

Company, Inc., May 1958.

Silverstein, 3.L., _(1957),

#Lineai-ized Theory of _{the Interaction}

of

Ships," Institute _{of Engineering}

Research, University of

_California,

May 1957.

Tuck, E.O., and _{Newman, J.N., (1974y}

'Hydrodynamic Interactions _Between

Ships," Proceedings _{of 10th Naval}

,...yIarcssosirtHdrod..ri,

_1974,

r

OTC 234

A Ellipse U-0.4 1.0 cs, 0.0 -2.0 0.4 0.0 3000

Fis. 1 - Definition sketch for

analysis via surface source distribution.

Ellipse ResultsOf, Tamentialization Surface Distributior Of Sources Alii1/411111CMII IMMINVAII211PIMEMINIAMINIIMMIIIIMIIIIMasirdw-mtamm

_{.2mimmmommumbewommwAstor}

Madl11111111111111011MMTAINIMMIIIIIP'

1101111111M=11111=MEM=

NOM -0.4 0 600 _{1200 1800} 2400 DISTANCE IN FEET

Fig. 2 - Comparison of loading functions as obtained from surface distribution of _{sources and from} tangentialization procedure. 3600 600 1200 _{1800 2400} 3000 3600 600 1200 1800 2400 _{3000 3600} -1.0

-Eaui-P-otential Lines

,

Undisturbed Region

.atisirea,nes,

ANDONwass.v..sigrai

411104041W

111.4111"1/11W

as

Fig. 31 - Elliptic cylinder moving in infinite but otherwise

stillfluid.

Fig. 5 - Definition sketchof fluid regions: at time of approaching ellipse,

The Intercepted StreamlineS - The Itlovimy Cylinder The Fixed Cylinder 'Transition Region The 'Moving, Cylinder

The Region Over Which PressureUs intensified-Transition__2/ Region -a< x < -2D .Attenuatedliegion The Fixed

wt.

_{Adimip, ' -}

_Cylinder

.-

4111444-attaPSW 1

$

..4 Region .6Ver Which Pressure Is intensified

Fig.4 - The assumedflowpattern during passing.

Fig.6 - Definition sketch oftiuid regions at

a time ofapproaching ellipse.

intercepted Stream! i'neN 'Undisturbed Reg ion

-Undisturbed! Region

xo< a

Fig. 8 - Definiticn sketch of fluid regtons at

timeof departing elliptic cylinder.

The Intercepted Streamlines _The Fixed, Cylinder The Moving Cylinder

The Region Over Which Pressure Is

.Intensified,

Just Before x = 0 Just Afterx = 0

Fig. 7 - Definition sketch at time when minor axes of symmetry of the passing ellipse and the fixed ellipse are nearly coincident.

The Intercepted Streamlines Undisturbed Region,' The Fixed Cylinder The Moving Cylinder

The Region Over Which, Pressure is Intensified

xo

Fig. 9 - Definition sketch of fluid regions at time of departing elliptic cylinder.

Fig. 10 KDving and fixed system coordinates

Undisturbed 'Region --a...ft._ 11111W-The

-0.4 -0.4 2.0 -2.0 0 4.0 Pulse 1 A . P .

PassingDirection.- Speed4 And 6 Knots

600

250 MDWT

600

150'

2231

Not, Measurements In Feet

Fixed IYawing Fixed

Point Ac_3r _entPoint

1200

1200

1800

1800

Test Set-uo Situation A

2400

2400

X

Fig. 11 - (a) Schematic (plan view) of overall experimental set-up. Test set-up situation A and (b)schematic of captive vessel.

3000 3000 3600 = 6.0 UA 4.0 0 600 1200 1800 2400 3000 3600 DISTANCE IN FEET

Fig. 12 - Comparison of loading function illustrating effect of varying passing ship speed.

(b) Passing Direction U-Spt.1.0 -AJA = =

_0.40 0

2,0

4,0

-4.0

0 600'

Fig. 13 - Comparison of' loading function, illustrating effect, of varying separation. distance.

1200 1800 2400 DISTANCE iN FEET "A. 1800' 240.0 A ' 3000f 3000 3600 3600 SenaratIon 'Distance: 150.0. Ft. -a-. 250.0 Ft..

350.0. Ft.

Under Keel Clearance/Draft,

0.30

_{-- 0.10}

----0.06

. -ift's (N C1 cc Ca. .40 2.0 0.0 -2.0 4.0 0.0 600 12.00 0 600 1200

43k' _{Fig., 14 - Comparison of loading functions illustrating effect or varying under .keel} clearance of restrained vessel.

4600' 1200 1800 2400 3000 3600 0.4 cvm 0.0 1800 2400 3000 3600 5000 3600 600 1200 1800 2400 DISTANCE IN 'FEET 600 1200 1800 2400 3000 3600 = 0.00 (1.401 0.0 - 4.

-0.4

_2.0

-2.0

4.0

-1.0

0 600 1200

1800

2400 DISTANCE IN FEET

3000

3600

Fig. 15 - Comparison of predicted (water depth/draft = 1.00) and measured (water depth/draft

= 1.06) loading functions. Predicted Measured 600 1200

1800

2400

3000

3600

1.5

Cx

1.0

0.9

0.6L

1.5

1.0

Cy

_0.8

0.6

0.4

0.2

1.5

1.0

0.8

0.6

CM

0.2

0.0

0.1

0.2

0.3

UNDER KEEL CLEARANCE TO DRAFT RATIO (MOORED OR PASSING WHICHEVER IS SMALLER)

0.4

0.5

Fig. 16 - Parameter curves of

dimensionless force and moment ratio vs water depth/draft ratio in zero current.

1.0

0.8

0.4

1.0

0.8

0.6

0.4

0.2

1.0

0.8

0.6

M

0.4

0 0

0.1

0.2

0.3

0.4

05

UNDER KEEL CLEARANCE TO DRAFT RATIO (MOORED OR PASSING WHICHEVER IS SMALLER)

Fig. 17 - Parameter curves of dimensionless force and moment ratio vs under keep clearance/draft ratio in 2 knot current.